Robust Beamforming and Time Allocation for Time-Division Cell-Free Near-Field ISAC

In this paper, we propose a time-division near-field integrated sensing and communication (ISAC) framework for cell-free multiple-input multiple-output (MIMO), where sensing and downlink communication are separated in time. During the sensing phase, user locations are estimated and used to construct location-aware channels, which are then exploited in the subsequent communication phase. By explicitly modeling the coupling between sensing-induced localization errors and channel-estimation errors, we capture the tradeoff between sensing accuracy and communication throughput. Based on this model, we jointly optimize the time-allocation ratio, sensing covariance matrix, and robust downlink beamforming under imperfect channel state information (CSI). The resulting non-convex problem is addressed via a semidefinite programming (SDP)-based reformulation within an alternating-optimization framework. To further reduce computational complexity, we also propose two low-complexity suboptimal designs: an error-ignorant scheme and a maximum ratio transmission (MRT)-based scheme. Simulation results show that the proposed scheme significantly improves localization accuracy over far-field and monostatic setups, thereby reducing channel estimation errors and ultimately enhancing the achievable rate. Moreover, the error-ignorant scheme performs well under stringent sensing requirements, whereas the MRT-based scheme remains robust over a wide range of sensing requirements by adapting the time-allocation ratio, albeit with some beamforming loss.